Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

Yang, Shan; Deng, Mou; Ren, Ruibin

doi:10.1186/s13662-020-2492-7

Cited by 12 publications

(5 citation statements)

References 35 publications

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“…In order to demonstrate more effectively that the proposed system has broken through the output saturation phenomenon of CTSR, and NPUATSR can achieve better performance, the fourth order Runge-Kutta algorithm [29] is used to conduct numerical simulation on three systems mentioned above. Let the system parameters a = 3, b = 4, c = 1, h = 1, w = 1 and the asymmetric factor λ = 0.5, it can obtain the output signal changes of the input signal when frequency f 0 = 0.01Hz and amplitude A ∈ [0.4, 3.6] after passing through the CTSR, NPUTSR and NPUATSR systems under the environment of noise intensity D = 0.…”

Section: The System Model Of Npuatsrmentioning

confidence: 99%

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Zhang

Zhu

zhang

2022

Meas. Sci. Technol.

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Early fault diagnosis of rolling bearings is of great significance in the application of mechanical equipment, which makes the extraction of weak fault signals particularly critical by stochastic resonance (SR). Compared with bistable SR, tristable SR has stronger advantages in weak signal extraction, but the classical tristable system (CTSR) was limited by output saturation, which resulted in insufficient signal amplification ability. To solve the above problems, combined with asymmetric system whose output can be improved to a higher degree, a novel piecewise unsaturated asymmetric tristable stochastic resonance (NPUATSR) system is proposed. Through numerical simulation, it is concluded that NPUATSR output amplitude varies proportionally with the amplitude of the input, which overcomes the output saturation of CTSR. Secondly, the stationary probability density and mean first passage time of particles are derived by using adiabatic approximation theory, and the variation law caused by parameters is analyzed in combination with potential function, the internal mechanism of the system is further studied. Through the output signal-to-noise ratio (SNR), it is found that the performance advantage of NPUTASR system is the most obvious, and different parameters affect the output SNR. Finally, the adaptive genetic algorithm is used to optimize the parameters, and the proposed system is applied to early fault diagnosis on different types of bearings. After comparison with different systems, the results show that NPUATSR can effectively detect the fault frequency, and has the most outstanding advantages in spectrum amplification and anti-noise performance, which proves that NPUATSR system has significant value in practical engineering application.

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Section: The System Model Of Npuatsrmentioning

confidence: 99%

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Zhang

Zhu

zhang

2022

Meas. Sci. Technol.

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“…The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/0264-4401.htm (Liang et al, 2018), inverse fractional advection-dispersion problem (Lobato et al, 2019), anomalous diffusion equations (Yang et al, 2019), risk theory (Constantinescu et al, 2019), HIV dynamics (Wasques et al, 2020), solution of mathematical equations using spline collocation methods (Zahra et al, 2020) and Langevin equation (Yang et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…In the past decades, different applications considering models represented by fractional order in different fields of science have been published in the literature. Among them, we can cite studies on chemistry (Kirchner et al , 2000), finance (Sabatelli et al , 2002; Bohner and Hatipoğlu, 2018, 2019), hydrology (Schumer et al , 2003), biology (Magin, 2006), viscoelasticity (Larsson et al , 2015), eigenvalue problem (Jin and Liu, 2016), robotics (Kumar and Rana, 2017), anomalous diffusion (Zhang et al , 2017), anomalous heat-diffusion problems (Yang et al , 2017a), advection-dispersion problems (Yuan et al , 2016; Zhang, 2018; Li and Rui, 2018), fractional Boussinesq equation (Yang et al , 2017b), diffusion equations (Yang et al , 2018; Shi et al , 2020), chaos synchronization (Su et al , 2018), anomalous advection-dispersion equations (Liang et al , 2018), inverse fractional advection-dispersion problem (Lobato et al , 2019), anomalous diffusion equations (Yang et al , 2019), risk theory (Constantinescu et al , 2019), HIV dynamics (Wasques et al , 2020), solution of mathematical equations using spline collocation methods (Zahra et al , 2020) and Langevin equation (Yang et al , 2020).…”

Section: Introductionmentioning

confidence: 99%

Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

Lima

Lobato

Steffen

2021

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PurposeIn this contribution, the solution of Mass-Spring-Damper Systems in the fractional context by using Caputo derivative and Orthogonal Collocation Method is investigated. For this purpose, different case studies considering constant and periodic sources are evaluated. The dimensional consistency of the model is guaranteed by introducing an auxiliary parameter. The obtained results are compared with those found by using both the analytical solution and the predictor-corrector method of Adams–Bashforth–Moulton type. The influence of the fractional order on the mechanical system is evaluated.Design/methodology/approachIn the present contribution, an extension of the Orthogonal Collocation Method to solve fractional differential equations is proposed.FindingsIn general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics.Originality/valueThe development of a new numerical method to solve fractional differential equations is the major contribution.

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“…In the treatment to these problems, electronic and technical developments are known to be of essential value across derivative structures. These systems have been recently considered to be basic tools in the development of various waveform travel formulas such as [24][25][26][27][28][29][30]. These are com-plex phenomena.…”

Section: Introductionmentioning

confidence: 99%

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

et al. 2020

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This research uses the extended exp-$( -\varphi(\vartheta ) ) $ ( − φ ( ϑ ) ) -expansion and the Jacobi elliptical function methods to obtain a fashionable explicit format for solutions to the fragmented biological population and the same width models that depict popular logistics because of deaths or births. In mathematical terminology, the linear, hyperbolic, and trigonometric equation solutions that have been found describe several innovative aspects from the two models. Sketching these solutions in different types is used to give them more details. The accuracy and performance of the method adopted show their ability to be applied to various nonlinear developmental equations.

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Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

Cited by 12 publications

References 35 publications

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

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